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We are told that number is Quantity in the primary sense,
number together with all continuous magnitude, space and time:
these are the standards to which all else that is considered as
Quantity is referred, including motion which is Quantity because
its time is quantitative- though perhaps, conversely, the time
takes its continuity from the motion.
If it is maintained that the continuous is a Quantity by the fact
of its continuity, then the discrete will not be a Quantity. If,
on the contrary, the continuous possesses Quantity as an
accident, what is there common to both continuous and discrete to
make them quantities?
Suppose we concede that numbers are quantities: we are merely
allowing them the name of quantity; the principle which gives
them this name remains obscure.
On the other hand, line and surface and body are not called
quantities; they are called magnitudes: they become known as
quantities only when they are rated by number-two yards, three
yards. Even the natural body becomes a quantity when measured, as
does the space which it occupies; but this is quantity
accidental, not quantity essential; what we seek to grasp is not
accidental quantity but Quantity independent and essential,
Quantity-Absolute. Three oxen is not a quantity; it is their
number, the three, that is Quantity; for in three oxen we are
dealing with two categories. So too with a line of a stated
length, a surface of a given area; the area will be a quantity
but not the surface, which only comes under that category when it
constitutes a definite geometric figure.
Are we then to consider numbers, and numbers only, as
constituting the category of Quantity? If we mean numbers in
themselves, they are substances, for the very good reason that
they exist independently. If we mean numbers displayed in the
objects participant in number, the numbers which give the count
of the objects- ten horses or ten oxen, and not ten units- then
we have a paradoxical result: first, the numbers in themselves,
it would appear, are substances but the numbers in objects are
not; and secondly, the numbers inhere in the objects as measures
[of extension or weight], yet as standing outside the objects
they have no measuring power, as do rulers and scales. If however
their existence is independent, and they do not inhere in the
objects, but are simply called in for the purpose of measurement,
the objects will be quantities only to the extent of
participating in Quantity.
So with the numbers themselves: how can they constitute the
category of Quantity? They are measures; but how do measures come
to be quantities or Quantity? Doubtless in that, existing as they
do among the Existents and not being adapted to any of the other
categories, they find their place under the influence of verbal
suggestion and so are referred to the so-called category of
Quantity. We see the unit mark off one measurement and then
proceed to another; and number thus reveals the amount of a
thing, and the mind measures by availing itself of the total
figure.
It follows that in measuring it is not measuring essence; it
pronounces its "one" or "two," whatever the character of the
objects, even summing contraries. It does not take count of
condition- hot, handsome; it simply notes how many.
Number then, whether regarded in itself or in the participant
objects, belongs to the category of Quantity, but the participant
objects do not. "Three yards long" does not fall under the
category of Quantity, but only the three.
Why then are magnitudes classed as quantities? Not because they
are so in the strict sense, but because they approximate to
Quantity, and because objects in which magnitudes inhere are
themselves designated as quantities. We call a thing great or
small from its participation in a high number or a low. True,
greatness and smallness are not claimed to be quantities, but
relations: but it is by their apparent possession of quantity
that they are thought of as relations. All this, however, needs
more careful examination.
In sum, we hold that there is no single genus of Quantity. Only
number is Quantity, the rest [magnitudes, space, time, motion]
quantities only in a secondary degree. We have therefore not
strictly one genus, but one category grouping the approximate
with the primary and the secondary.
We have however to enquire in what sense the abstract numbers are
substances. Can it be that they are also in a manner
quantitative? Into whatever category they fall, the other numbers
[those inherent in objects] can have nothing in common with them
but the name.
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